Matrix analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Probabilistic Languages: A Review and Some Open Questions
ACM Computing Surveys (CSUR)
A study of tree adjoining grammars
A study of tree adjoining grammars
Stochastic lexicalized tree-adjoining grammars
COLING '92 Proceedings of the 14th conference on Computational linguistics - Volume 2
Estimation of consistent probabilistic context-free grammars
HLT-NAACL '06 Proceedings of the main conference on Human Language Technology Conference of the North American Chapter of the Association of Computational Linguistics
IWPT '09 Proceedings of the 11th International Conference on Parsing Technologies
Consistency of stochastic context-free grammars
Mathematical and Computer Modelling: An International Journal
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Much of the power of probabilistic methods in modelling language comes from their ability to compare several derivations for the same string in the language. An important starting point for the study of such cross-derivational properties is the notion of consistency. The probability model defined by a probabilistic grammar is said to be consistent if the probabilities assigned to all the strings in the language sum to one. From the literature on probabilistic context-free grammars (CFGs), we know precisely the conditions which ensure that consistency is true for a given CFG. This paper derives the conditions under which a given probabilistic Tree Adjoining Grammar (TAG) can be shown to be consistent. It gives a simple algorithm for checking consistency and gives the formal justification for its correctness. The conditions derived here can be used to ensure that probability models that use TAGs can be checked for deficiency (i.e. whether any probability mass is assigned to strings that cannot be generated).